From the symptoms,the small bumps around lips can be Fordyce spots.The cuts on the lips are due to cheilitis. Fordyce spots are yellowish-white granules on the inner surface and border of the lips.Treatment of Fordyce spots includes CO2 laser or electro desiccation, TCA chemical peels(temporary treatment),diathermy or laser vaporization.
Avoid licking the lips as saliva evaporates quickly resulting in them being drier than before. Drink plenty of water and take multivitamin supplements and do not apply lipstick or other cosmetic products for some days. Use a humidifier to moisturize the air in your home and apply shea butter or Vaseline on your lips.
If the symptoms persist then pls consult a dermatologist.
I hope it helps.Take care and pls do keep me posted on how you are doing or if you have any additional doubts.Kind regards.